A new optical encoding method for labeling large numbers of samples based on measurement of emission ratios in samples containing various ratios of rare earth infrared upconverting phosphor (RUP) labels is described. Preliminary data suggest it may be possible to multiplex >2.5 x 104 samples using a four colors system. While previous examples of labeling individual samples with a single RUP material are known, the use of multiplexing based on the ratios of more than one RUP within a single reporter particle vastly expands the number of individual samples that can be identified. The presence of non-overlapping, very narrow emissions in the visible region for the rare earth emitters, lack of sample autofluorescence at the 980 nm excitation wavelength and the total absence of photobleaching makes the high degree of multiplexing possible. To perform a 10,000 oligonucleotide microarray experiment in a test tube, the 10,000 oligonucleotides of interest could be attached to 10,000 different RUP samples and subjected to normal hybridization. Analysis of the red/green target ratio and the RUP label, on two separate detectors within a flow cytometer capable of sorting 8-10 thousand samples/second, could allow millions of gene expression products to be analyzed in a few minutes. [unreadable] [unreadable]